不解方程,求下列方程兩根之和與兩根之積:
(1)4x2+1=7x,x1+x2=______,x1•x2=______.
(2)3x2-1=0,x1+x2=______,x1•x2=______.
(3)x2-6x=0,x1+x2=______,x1•x2=______.
(4)2x2-(m+1)x-m=0,x1+x2=______,x1•x2=______.
解:(1)先把方程化為:4x
2-7x+1=0,∴x
1+x
2=
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,x
1•x
2=
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,
(2)根據(jù)根與系數(shù)的關系得:x
1+x
2=0,x
1•x
2=-
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.
(3)根據(jù)根與系數(shù)的關系得:x
1+x
2=6,x
1•x
2=0.
(4)根據(jù)根與系數(shù)的關系得:x
1+x
2=
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,x
1•x
2=
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.
故答案為:
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,
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;0,-
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;6,0;
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,-
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.
分析:(1)先把方程化為4x
2-7x+1=0的形式,根據(jù)根與系數(shù)的關系即可解題.
(2)根據(jù)根與系數(shù)的關系即可解題.
(3)根據(jù)根與系數(shù)的關系即可解題.
(4)根據(jù)根與系數(shù)的關系即可解題.
點評:本題考查了根與系數(shù)的關系,屬于基礎題,關鍵掌握x
1,x
2是一元二次方程ax
2+bx+c=0(a≠0)的兩根時,x
1+x
2=-
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,x
1x
2=
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.